Welcome to MathOverflow

Question

3

See http://math.uni.lu/~wiese/galois/Boeckle-Luxemburg-Notes.pdf, Theorem 1.4(a): Is there an example of a semisimple $\mathbf{Q}_\ell$-representation $V$ of $G_F$ ($F$ a global field) ramified at a set $S$ of places where $S$ is not finite (for every $\dim{V} \geq 1$)?

edited Aug 19 at 22:58

Jim Humphreys
26.1k●38●84

asked Aug 18 at 18:59

Timo Keller
2,621●4●17

2

For $\mathrm{dim}(V) = 2$, see: jstor.org/stable/40067979. For $\mathrm{dim}(V) \ge 2$, take symmetric powers. – Lavender Honey Aug 18 at 20:38

@Timo: I've added a tag and would also urge you to incorporate your own "answer" into an edited question to avoid confusion and focus the question better. – Jim Humphreys Aug 19 at 23:00

Timo Keller · Answer 1 · 2012-08-18 20:08:28Z UTC

2

It seems that for $\dim{V} = 1$, there is no such representation http://www.math.leidenuniv.nl/scripties/KretMaster.pdf p. 10.

edited Aug 18 at 20:08

answered Aug 18 at 19:25

Timo Keller
2,621●4●17

Is there a semisimple $\mathbf{Q}_\ell$-representation of $G_F$ ramified at an infinite set of places?

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.